Yet to admit beer finally finished (7)
I believe the answer is:
through
'finished' is the definition.
(I've seen this before)
'yet to admit beer finally' is the wordplay.
'yet' becomes 'though'.
'to admit' is an insertion indicator.
'finally' indicates one should take the final letters.
The final letter of 'beer' is 'r'.
'though' enclosing 'r' is 'THROUGH'.
(Other definitions for through that I've seen before include "No longer going out together" , "From one end or side to the other" , "As a result of" , "By way of - exhausted" , "done" .)